"By the end of 2014 I would like to see half of our local radio stations with a woman presenting on the breakfast shows," he said.

Radio Times said that of 41 breakfast shows – the target does not take into account radio stations outside England and the Channel Islands – there are now 17 female presenters and an 18th is in the pipeline, compared to eight before the BBC boss made the pledge.

But it said that, of the 18 shows (44 per cent) with a female presenter, only five feature women presenting on their own.

David Holdsworth, the BBC's controller of English regions, said that the broadcaster had made "demonstrably good progress" and he was confident of reaching 50 per cent by the end of the year.

But he admitted that he had been contacted by a few worried male presenters asking: "Is the game up for me?"

And he added: "There's a much bigger job to do, which is about the overall sound of BBC local radio. And that's not just about women; it's about age, people's ethnic background, disability, social class. What you really want are presenters who are a good balance on all those measures."